WAEC Mathematics Syllabus for WASSCE 2027

Our summary: Writing numbers in bases other than ten and doing arithmetic in them.

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• Conversion from one base to base 10 and vice versa.
• Conversion from one base to another base.
• Addition, subtraction, and multiplication of number bases.

Our summary: Working with remainders after division, like days of the week or hours on a clock.

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• Interpretation of modulo arithmetic e.g. $6 + 4 = k \pmod 7$, $3 \times 5 = b \pmod 6$, $m \equiv 2 \pmod 3$, etc.
• Relate to market days, clock, shift duty, etc.

Our summary: Adding, subtracting, multiplying and dividing fractions and decimals, and rounding sensibly.

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• Approximations should be realistic, e.g. a road is not measured correctly to the nearest cm.

Our summary: The rules for powers, and writing very large or very small numbers in standard form.

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• e.g. $a^x \times a^y = a^{x+y}$, $a^x \div a^y = a^{x-y}$, $(a^x)^y = a^{xy}$, etc. where $x, y$ are real numbers and $a \neq 0$.
• Include simple examples of negative and fractional indices.
• Expression of large and small numbers in standard form, e.g. $375300000 = 3.753 \times 10^8$, $0.00000035 = 3.5 \times 10^{-7}$.
• Use of tables of squares, square roots, and reciprocals is accepted.

Our summary: Logarithms as the reverse of powers, and using their rules to simplify calculations.

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• Calculations involve multiplication, division, powers, and roots.

Our summary: Spotting patterns in lists of numbers and working with arithmetic and geometric progressions.

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• Determine any term of a given sequence.
• The notation $U_n$ = the nth term of a sequence may be used.
• Simple cases only, including word problems. (Include sum for A.P. and exclude sum for G.P.)

Our summary: Grouping things into sets and using Venn diagrams to solve everyday counting problems.

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• Notations: ℰ, ⊂, ∪, ∩, { }, ∅, P′ (the complement of P).
• Properties, e.g. commutative, associative, and distributive.
• Use of Venn diagrams restricted to at most 3 sets.

Our summary: Deciding whether statements are true or false and how one statement leads to another.

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• Use of symbols: ⟹, ⟸, use of Venn diagrams.

Our summary: Doing the four basic operations with whole numbers, negatives and fractions, and placing them on a number line.

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• Match rational numbers with points on the number line.
• Notation: Natural numbers (N), Integers (Z), Rational numbers (Q).

Our summary: Simplifying square-root expressions that do not come out as whole numbers.

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• Surds of the form $\frac{a}{\sqrt{b}}$, $a\sqrt{b}$ and $a \pm \sqrt{b}$ where $a$ is a rational number and $b$ is a positive integer.
• Basic operations on surds (exclude surd of the form $\frac{a}{b + c\sqrt{d}}$).

Our summary: Arranging numbers in grids, combining them, and using determinants to solve pairs of equations.

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• Not more than 3 × 3 matrices. Idea of columns and rows.
• Restrict to 2 × 2 matrices.
• Application to solving simultaneous linear equations in two variables. Restrict to 2 × 2 matrices.

Our summary: Comparing quantities, sharing them in proportion, and working with rates such as speed, tax and exchange.

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• Relate to real-life situations.
• Include average rates, taxes, e.g. VAT, withholding tax, etc.

Our summary: Using percentages for interest, discounts, profit and loss and similar money problems.

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• Limit compound interest to a maximum of 3 years.

Our summary: Basic money-over-time ideas such as depreciation, annuities, shares and bonds.

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• Definition/meaning, calculation of depreciation on fixed assets, computation of amortisation on capitalised assets.
• Definition/meaning, solve simple problems on annuities.
• Shares/stocks, debentures, bonds, simple problems on interest on bonds and debentures.

Our summary: How one quantity changes when another changes, directly, inversely, jointly or partly.

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• Expression of various types of variation in mathematical symbols, e.g. direct ($z \propto n$), inverse ($z \propto \frac{1}{n}$), etc.
• Application to simple practical problems.

Our summary: Turning a word situation into an algebraic expression and finding its value.

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• e.g. find an expression for the cost C Naira of 4 pens at x Naira each and 3 oranges at y Naira each. Solution: $C = 4x + 3y$.
• e.g. if $x = 60$ and $y = 20$, find C. $C = 4(60) + 3(20) = 300$ naira.

Our summary: Expanding brackets, factorising, and using made-up operations on numbers.

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• e.g. $(a + b)(c + d)$, $(a + 3)(c - 4)$, etc.
• Factorisation of expressions of the form $ax + ay$, $a(b + c) + d(b + c)$, $a^2 - b^2$, $ax^2 + bx + c$ where $a, b, c$ are integers.
• Application of difference of two squares, e.g. $49^2 - 47^2 = (49 + 47)(49 - 47) = 96 \times 2 = 192$.
• Perform binary operations on real numbers, such as $a * b = 2a + b - ab$, etc.

Our summary: Solving one equation or a pair of equations to find the unknowns.

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• Solving/finding the truth set (solution set) for linear equations in one variable.
• Solving/finding the truth set of simultaneous equations in two variables by elimination, substitution and graphical methods.
• Word problems involving one or two variables.

Our summary: Rearranging a formula to make a different letter the answer, then putting in values.

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• e.g. if $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$, find $v$.
• Finding the value of a variable, e.g. evaluating $v$ given the values of $u$ and $f$.

Our summary: Solving equations with a squared term and building one from its roots.

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• Using factorisation, i.e. $ab = 0 \Rightarrow$ either $a = 0$ or $b = 0$.
• By completing the square and use of formula.
• Simple rational roots only, e.g. forming a quadratic equation whose roots are $-3$ and $\frac{5}{2}$ $\Rightarrow (x + 3)(x - \frac{5}{2}) = 0$.

Our summary: Reading and drawing straight-line and curved graphs and using them to find solutions and gradients.

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• Finding: (i) the coordinates of maximum and minimum points on the graph; (ii) intercepts on the axes, identifying the axis of symmetry, recognising sketched graphs.
• Use of quadratic graphs to solve related equations, e.g. graph of $y = x^2 + 5x + 6$ to solve $x^2 + 5x + 4 = 0$.
• Determining the gradient by drawing relevant triangles.

Our summary: Solving "greater than" and "less than" problems, on a number line and on a graph.

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• A truth set is also required.
• Simple practical problems.
• Maximum and minimum values. Application to real-life situations, e.g. minimum cost, maximum profit, linear programming, etc.

Our summary: Adding and simplifying fractions that have letters in them.

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• Simple cases only e.g. $\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}$ ($x \neq 0$, $y \neq 0$).
• Simple cases only e.g. $\frac{1}{x - a} + \frac{1}{x - b} = \frac{2x - a - b}{(x - a)(x - b)}$ where $a$ and $b$ are constants and $x \neq a$ or $b$.
• Values for which a fraction is undefined, e.g. $\frac{1}{x + 3}$ is not defined for $x = -3$.

Our summary: The different ways inputs can be matched to outputs and how to find the rule.

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• One-to-one, one-to-many, many-to-one, many-to-many.
• Functions as a mapping, determination of the rule of a given mapping/function.

Our summary: Finding lengths and distances, including arcs, sectors and distances on the Earth's surface.

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• No formal proofs of the theorem and rules are required.
• Distances along latitudes and longitudes and their corresponding angles.

Our summary: Finding the area of flat shapes and the surface area of solids.

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• Areas of similar figures.
• Include area of triangle = ½ base × height and $\frac{1}{2}ab\sin C$.
• Areas of compound shapes.
• Relationship between the sector of a circle and the surface area of a cone.

Our summary: Finding how much space solid shapes take up.

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• Include volumes of compound shapes.

Our summary: The basic rules for angles at a point, on a straight line and where lines cross.

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• The degree as a unit of measure.
• Consider acute, obtuse, reflex angles, etc.

Our summary: Which angles are equal or add up to 180° when a line crosses parallel lines.

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• Application to proportional division of a line segment.

Our summary: The angle and side rules for triangles, special quadrilaterals and other polygons.

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• The formal proofs of those underlined may be required.
• Underlined in the syllabus: the angle sum of a triangle is 2 right angles; the exterior angle of a triangle equals the sum of the two interior opposite angles.
• Conditions to be known but proofs not required, e.g. SSS, SAS, etc.
• Use symmetry where applicable.
• Equiangular properties and ratio of sides and areas.
• Sum of interior angles = $(n - 2) \times 180°$ or $(2n - 4)$ right angles, where $n$ is the number of sides.

Our summary: The angle and tangent rules that hold for chords, arcs and tangents of a circle.

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• Angles subtended by chords in a circle and at the centre.
• Perpendicular bisectors of chords.
• The formal proofs of those underlined may be required.
• Underlined in the syllabus: the angle at the centre is twice that at the circumference; angles in opposite segments are supplementary; the alternate segment theorem (tangent-chord angle).

Our summary: Drawing angles, lines, triangles and quadrilaterals accurately with a ruler and compasses.

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• Include combination of these angles, e.g. 75°, 105°, 135°, etc.

Our summary: Finding every point that follows a given distance rule and where such rules meet.

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• Consider parallel and intersecting lines.
• Application to real-life situations.

Our summary: Finding distance, midpoint, gradient and equation of a line from coordinates.

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• The midpoint of two points, distance between two points, i.e. $|PQ| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ where $P(x_1, y_1)$ and $Q(x_2, y_2)$.
• Gradient (slope) of a line $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Equation of a line in the form $y = mx + c$ and $y - y_1 = m(x - x_1)$, where $m$ is the gradient (slope) and $c$ is a constant.

Our summary: The three basic trig ratios, their values for common angles and their graphs.

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• Use of right-angled triangles.
• Without the use of tables.
• Relate to the unit circle. $0° \leq x \leq 360°$. e.g. $y = a\sin x$, $y = b\cos x$.
• Graphs of simultaneous linear and trigonometric equations, e.g. $y = a\sin x + b\cos x$, etc.

Our summary: Using trig to find heights and distances from looking up or down at something.

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• Simple problems only.

Our summary: Giving directions as angles from north and working out distances and angles from them.

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• Notation e.g. 035°, N35°E.
• Simple problems only.
• Use of a diagram is required.
• Sine and cosine rules may be used.

Our summary: Finding the rate of change of simple expressions and the reverse process.

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• Concept/meaning of differentiation/derived function, $\frac{dy}{dx}$, relationship between the gradient of a curve at a point and the differential coefficient of the equation of the curve at that point.
• Standard derivatives of some basic functions, e.g. if $y = x^2$, $\frac{dy}{dx} = 2x$. If $s = 2t^3 + 4$, $\frac{ds}{dt} = v = 6t^2$, where $s$ = distance, $t$ = time and $v$ = velocity.
• Application to real-life situations, such as maximum and minimum values, rates of change, etc.
• Meaning/concept of integration, evaluation of simple definite algebraic equations.

Our summary: Organising data into tables and charts and summarising it with averages and spread.

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• Construction of frequency distribution tables, concept of class intervals, class mark and class boundary.
• Reading and drawing simple inferences from graphs, interpretation of data in histograms.
• Exclude unequal class interval.
• Use of an assumed mean is acceptable but not required.
• For grouped data, the mode should be estimated from the histogram while the median, quartiles and percentiles are estimated from the cumulative frequency curve.
• Application of the cumulative frequency curve to everyday life.
• Definition of range, variance, standard deviation, and interquartile range.
• Note that mean deviation is the mean of the absolute deviations from the mean, and variance is the square of the standard deviation.
• Problems on range, variance, standard deviation, etc.
• Standard deviation of grouped data.

Our summary: Working out the chance of events, alone or combined.

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• Include equally likely events, e.g. probability of throwing a six with a fair die or a head when tossing a fair coin.
• With replacement, without replacement.
• Simple practical problems only.
• Interpretation of "and" and "or" in probability.

Our summary: Quantities with size and direction, written as columns and combined by adding and scaling.

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• (5, 060°), e.g. $\begin{pmatrix} 5\sin(60^\circ) \\ 5\cos(60^\circ) \end{pmatrix}$.
• Knowledge of graphical representation is necessary.

Our summary: Moving or resizing shapes on a grid by reflecting, rotating, translating or enlarging them.

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• Restrict plane to the x and y axes and the lines $x = k$, $y = x$ and $y = kx$, where $k$ is an integer. Determination of mirror lines (symmetry).
• Rotation about the origin and a point other than the origin. Determination of the angle of rotation (restrict angles of rotation to $-180°$ to $180°$).
• Translation using a translation vector.
• Draw the images of plane figures under enlargement with a given centre for a given scale factor. Use the given scales to enlarge or reduce plane figures.